Binding of Tat protein to TAR RNA is necessary for effective replication of HIV-1. In order to identify potential inhibitors of Tat/TAR interaction we use Monte-Carlo search in torsion angle space for docking of compounds from the Available Chemical Directory (ACD) on TAR. In order to validate the procedure we performed docking of ligands for five RNA complexes of known structure. In the cases where water molecules are not crucial for binding, the experimental structures were successfully reproduced. An empirical binding free energy function was developed, which accounts for solvation and for change of torsion angle entropy. As a validation test we screened the ACD for ligands for L-arginine RNA aptamer. The native ligand was ranked 17 out of 110,000. Screening of the ACD for TAR ligands gave very good ranks to all known TAR ligands. Several best ranked compounds were tested for inhibition of Tat-TAR interaction. Two of them showed IC50 of ca. 1 uM. This docking method is very effective for database screening for RNA ligands. With reasonable run-times, the final list of compounds can be thousands times smaller then the original database and still contain the ntive ligand.